Problem: The following line passes through point $(6, -6)$ : $y = -\dfrac{9}{13} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(6, -6)$ into the equation gives: $-6 = -\dfrac{9}{13} \cdot 6 + b$ $-6 = -\dfrac{54}{13} + b$ $b = -6 + \dfrac{54}{13}$ $b = -\dfrac{24}{13}$ Plugging in $-\dfrac{24}{13}$ for $b$, we get $y = -\dfrac{9}{13} x - \dfrac{24}{13}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(6, -6)$